A shopkeeper bought 12 pens for ₹ 200 and sold 8 for ₹ 160. His gain or loss…

Concept

Profit or loss percent is always measured against the cost price on a common (per-unit) basis: Profit/Loss % = ((SP − CP) / CP) × 100. When the quantity bought and the quantity sold are different, first reduce both the cost and the selling price to a per-unit (per-pen) rate before comparing them — comparing two different total amounts directly, without reducing to the same unit, gives a wrong percentage.

Application

1. Cost price of 12 pens = ₹200, so cost price per pen = 200 ÷ 12 = ₹50/3 (≈ ₹16.67).

2. Selling price of 8 pens = ₹160, so selling price per pen = 160 ÷ 8 = ₹20.

3. Profit per pen = selling price per pen − cost price per pen = 20 − 50/3 = 10/3.

4. Profit % = (profit per pen ÷ cost price per pen) × 100 = (10/3 ÷ 50/3) × 100 = (10 ÷ 50) × 100 = 20% exactly.

Cross-check

Scale both transactions up to a common quantity — the LCM of 12 and 8, which is 24 pens — and verify with whole totals instead of per-unit rates:

• Cost of 24 pens at the buying rate = 24 × (200 ÷ 12) = ₹400.

• Selling price of 24 pens at the selling rate = 24 × (160 ÷ 8) = ₹480.

• Profit = 480 − 400 = ₹80, so profit % = (80 ÷ 400) × 100 = 20%, confirming the per-unit method above.

So the shopkeeper makes a 20% profit.